A Flux-Limited Model for Glioma Patterning with Hypoxia-Induced Angiogenesis

Pawan Kumar,Christina Surulescu

doi:10.3390/sym12111870

Abstract

We propose a model for glioma patterns in a microlocal tumor environment under the influence of acidity, angiogenesis, and tissue anisotropy. The bottom-up model deduction eventually leads to a system of reaction–diffusion–taxis equations for glioma and endothelial cell population densities, of which the former infers flux limitation both in the self-diffusion and taxis terms. The model extends a recently introduced (Kumar, Li and Surulescu, 2020) description of glioma pseudopalisade formation with the aim of studying the effect of hypoxia-induced tumor vascularization on the establishment and maintenance of these histological patterns which are typical for high-grade brain cancer. Numerical simulations of the population level dynamics are performed to investigate several model scenarios containing this and further effects.

Highlights

Classification of glioma, the most common type of primary brain tumors, typically comprises four grades, according to the degree of malignancy [1,2]
The highest grade, IV, corresponds to characteristic histological patterns called pseudopalisades; they exhibit garland-like hypercellular structures surrounding necrotic regions usually centered around one or several sites of vaso-occlusion [3,4,5,6], and they are associated with poor patient survival prognosis [1]
The vast majority of continuous models for cell migration involve reaction-diffusion(-taxis) partial differential equation (PDE) on the macroscopic scale, irrespective to whether those equations were obtained by a direct formulation or a more or less formal deduction from lower scales

Summary

Introduction

Classification of glioma, the most common type of primary brain tumors, typically comprises four grades, according to the degree of malignancy [1,2]. Hypoxia around the pseudopalisading cells triggers the process of capillary formation, which involves a cascade of coordinated steps [7,8]. It typically starts with tumor cells overexpressing hypoxia-inducible regulators of angiogenesis, including vascular endothelial growth factor (VEGF) [4]. The latter acts as a chemoattractant and proliferation promotor for endothelial cells (ECs) lining the surrounding blood vessels. Understanding the mechanisms of tumor malignancy can contribute to development and tuning of therapeutic strategies, e.g., by targeting angiogenesis [10] or by tumor alkalization [11] used in a (neo)adjuvant way to other approaches (such as surgery and radiotherapy)

Objectives

Methods

Conclusion